(5-7i+i²) + (8i³+12) The complex expression above is equivalent to the expression a+bi, for the integer constants a and b. What is the value of a?

16-15i

Explanation:

(5-7i+i²) + (8i³+12)

i²= -1 and i³=-i, so we can substitute those in and rewrite the equation as

(5-7i-1) + (-8i+12)

We can now drop the parentheses because there is no multiplication or distribution involved.

5-7i-1 + -8i+12

And just rearrange the order of the terms to make it easier to combine like terms. Just remember to keep negative signs with the correct terms.

5-1+12-7i-8i

And now combine like terms

16-15i